Book:Gert K. Pedersen/Analysis Now/Second Edition
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Gert K. Pedersen: Analysis Now (2nd Edition)
Published $\text {1995}$, Springer
- ISBN 978-0387967882
Subject Matter
Contents
Preface
- Chapter 1: General Topology
- 1.1 Ordered Sets
- 1.2 Topology
- 1.3 Convergence
- 1.4 Continuity
- 1.5 Separation
- 1.6 Compactness
- 1.7 Local Compactness
- Chapter 2: Banach Spaces
- 2.1 Normed Spaces
- 2.2 Category
- 2.3 Dual Spaces
- 2.4 Seminormed Spaces
- 2.5 $w^*$-compactness
- Chapter 3: Hilbert Spaces
- 3.1 Inner products
- 3.2 Operators on Hilbert Space
- 3.3 Compact Operators
- 3.4 The Trace
- Chapter 4: Spectral Theory
- 4.1 Banach Algebras
- 4.2 The Gelfand Transform
- 4.3 Function Algebras
- 4.4 The Spectral Theorem, I
- 4.5 The Spectral Theorem, II
- 4.6 Operator Algebra
- 4.7 Maximal Commutative Algebras
- Chapter 5: Unbounded Operators
- 5.1 Domains, Extensions and Graphs
- 5.2 The Cayley Transform
- 5.3 Unlimited Spectral Theory
- Chapter 6: Integration Theory
- 6.1 Radon Integrals
- 6.2 Measurability
- 6.3 Measures
- 6.4 $L^p$ spaces
- 6.5 Duality theory
- 6.6 Product Intergrals
Bibliography
List of Symbols
Index